Greek has nothing to do with the probiotics. It has less water which is how the higher microbe/protein content can be attributed. It is traditionally pressed in cheese cloth to remove water content. You can buy probiotics in gel caps if you believe you are deficient. I am not saying that good yogurt doesn’t help. I eat plain greek yogurt every week.
Fermented foods like yogurt can have lots of beneficial bacteria (pro-biotics for the squeamish). Before it’s packaged most food manufacturers heat (pasteurize) the yogurt to kill the bacteria and extend the shelf life. Greek yogurt has less water but is not necessarily more pro-biotic. It doesn’t matter when you eat it.
The more diverse your diet the more diverse you gut bacteria (microbiome) and that’s good.
Fruits and vegetables have more of what your microbiome eats.
Eat more fruit and vegs - improve your gut health.
A healthy gastrointestinal microbiome is dependent on dietary diversity
I would recommend this video for you, the guy they are interviewing is a leading researcher in the gut microbiome. https://youtu.be/uoVNKT76MUc Full disclosure, I just ordered one of their bundles they recommended for me in my endeavor to solve my GI issues.
This opinion is loosely based on science.
Humans have highly acidic stomach acid at 1.5ph… which is actually very high even from a predatory standpoint… that ph becomes more basic(ph raises) with a large meal… probiotics have better survivability with a large meal.
Where it might change is that it might take longer for the stomach to empty leaving the probiotic in the stomach longer.
So in my theory eat yogurt with a meal but consider these topics
Probiotics need their own food in the gut to flourish. If consumed alone the bacteria will not survive past the stomach given the high acidity and lack of fiber for the probiotics to feed from. It’s best to mix yogurt or any other probiotic rich food with fruit and grains which offer a complex fiber make up well enough to gain the benefits from the healthy bacteria. Fiber gives the probiotics a place to latch on and thrive past the stomach into the small and large intestine before you poop it out.